Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r21792 = m;
        double r21793 = 1.0;
        double r21794 = r21793 - r21792;
        double r21795 = r21792 * r21794;
        double r21796 = v;
        double r21797 = r21795 / r21796;
        double r21798 = r21797 - r21793;
        double r21799 = r21798 * r21794;
        return r21799;
}
↓
double f(double m, double v) {
        double r21800 = 1.0;
        double r21801 = m;
        double r21802 = v;
        double r21803 = r21801 / r21802;
        double r21804 = r21800 * r21803;
        double r21805 = 2.0;
        double r21806 = pow(r21801, r21805);
        double r21807 = r21806 / r21802;
        double r21808 = r21800 + r21807;
        double r21809 = r21804 - r21808;
        double r21810 = r21800 - r21801;
        double r21811 = r21809 * r21810;
        return r21811;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]
  4. Using strategy rm

  5. Applied div-inv0.1

    \[\leadsto \left(\frac{m}{\color{blue}{v \cdot \frac{1}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]

  6. Applied associate-/r*0.1

    \[\leadsto \left(\color{blue}{\frac{\frac{m}{v}}{\frac{1}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]

  7. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right)} \cdot \left(1 - m\right)\]

  8. Final simplification0.1

    \[\leadsto \left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2019297 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))